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revision 1.4 by adcroft, Tue Nov 13 18:22:24 2001 UTC revision 1.11 by jmc, Tue Jan 15 18:41:46 2008 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: Centennial Time Scale Sensitivities}  \section{Centennial Time Scale Tracer Injection}
5    \label{www:tutorials}
6    \label{sect:eg-simple-tracer}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-simple-tracer: -->
9    \end{rawhtml}
10    \begin{center}
11    (in directory: {\it verification/tutorial\_tracer\_adjsens/})
12    \end{center}
13    
14  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
15    
# Line 16  Line 24 
24  %\end{center}  %\end{center}
25    
26  \subsection{Introduction}  \subsection{Introduction}
27    \label{www:tutorials}
28    
 This document describes the fourth example MITgcm experiment.  
29  This example illustrates the use of  This example illustrates the use of
30  the MITgcm to perform sensitivity analysis in a  the MITgcm to perform sensitivity analysis in a
31  large scale ocean circulation simulation.  large scale ocean circulation simulation.
32    The files for this experiment can be found in the
33    verification directory under tutorial\_tracer\_adjsens.
34    
35  \subsection{Overview}  \subsection{Overview}
36    \label{www:tutorials}
37    
38  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
39  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
# Line 48  Altogether, this yields the following fo Line 59  Altogether, this yields the following fo
59  in the model surface layer.  in the model surface layer.
60    
61  \begin{eqnarray}  \begin{eqnarray}
62  \label{EQ:global_forcing}  \label{EQ:eg-simple-tracer-global_forcing}
63  \label{EQ:global_forcing_fu}  \label{EQ:eg-simple-tracer-global_forcing_fu}
64  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
65  \\  \\
66  \label{EQ:global_forcing_fv}  \label{EQ:eg-simple-tracer-global_forcing_fv}
67  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
68  \\  \\
69  \label{EQ:global_forcing_ft}  \label{EQ:eg-simple-tracer-global_forcing_ft}
70  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
71   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
72  \\  \\
73  \label{EQ:global_forcing_fs}  \label{EQ:eg-simple-tracer-global_forcing_fs}
74  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
75   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
76  \end{eqnarray}  \end{eqnarray}
# Line 81  The configuration is illustrated in figu Line 92  The configuration is illustrated in figu
92    
93    
94  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
95    \label{www:tutorials}
96    
97    
98   The model is configured in hydrostatic form.  The domain is discretised with   The model is configured in hydrostatic form.  The domain is discretised with
# Line 118  $ Line 130  $
130   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
131  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
132  The implicit free surface form of the pressure equation described in Marshall et. al  The implicit free surface form of the pressure equation described in Marshall et. al
133  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
134  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
135  \\  \\
136    
137  Wind-stress momentum inputs are added to the momentum equations for both  Wind-stress momentum inputs are added to the momentum equations for both
138  the zonal flow, $u$ and the meridional flow $v$, according to equations  the zonal flow, $u$ and the meridional flow $v$, according to equations
139  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:eg-simple-tracer-global_forcing_fu}) and (\ref{EQ:eg-simple-tracer-global_forcing_fv}).
140  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations for
141  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
142  (\ref{EQ:global_forcing_ft}) and (\ref{EQ:global_forcing_fs}).  (\ref{EQ:eg-simple-tracer-global_forcing_ft}) and (\ref{EQ:eg-simple-tracer-global_forcing_fs}).
143  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
144  % {\fracktur}  % {\fracktur}
145    
146    
147  \begin{eqnarray}  \begin{eqnarray}
148  \label{EQ:model_equations}  \label{EQ:eg-simple-tracer-model_equations}
149  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
150    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
151    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}
# Line 174  elevation $\eta$ and the hydrostatic pre Line 186  elevation $\eta$ and the hydrostatic pre
186  \\  \\
187    
188  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
189    \label{www:tutorials}
190    
191  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
192  This value is chosen to yield a Munk layer width \cite{adcroft:95},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
193    
194  \begin{eqnarray}  \begin{eqnarray}
195  \label{EQ:munk_layer}  \label{EQ:eg-simple-tracer-munk_layer}
196  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
197  \end{eqnarray}  \end{eqnarray}
198    
# Line 193  time step $\delta t=1200$secs. With this Line 206  time step $\delta t=1200$secs. With this
206  parameter to the horizontal Laplacian friction \cite{adcroft:95}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
207    
208  \begin{eqnarray}  \begin{eqnarray}
209  \label{EQ:laplacian_stability}  \label{EQ:eg-simple-tracer-laplacian_stability}
210  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
211  \end{eqnarray}  \end{eqnarray}
212    
# Line 205  for stability. Line 218  for stability.
218  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
219    
220  \begin{eqnarray}  \begin{eqnarray}
221  \label{EQ:laplacian_stability_z}  \label{EQ:eg-simple-tracer-laplacian_stability_z}
222  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
223  \end{eqnarray}  \end{eqnarray}
224    
# Line 219  and vertical ($K_{z}$) diffusion coeffic Line 232  and vertical ($K_{z}$) diffusion coeffic
232  \cite{adcroft:95}  \cite{adcroft:95}
233    
234  \begin{eqnarray}  \begin{eqnarray}
235  \label{EQ:inertial_stability}  \label{EQ:eg-simple-tracer-inertial_stability}
236  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
237  \end{eqnarray}  \end{eqnarray}
238    
# Line 232  horizontal flow Line 245  horizontal flow
245  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
246    
247  \begin{eqnarray}  \begin{eqnarray}
248  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-cfl_stability}
249  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
250  \end{eqnarray}  \end{eqnarray}
251    
# Line 244  limit of 0.5. Line 257  limit of 0.5.
257  \cite{adcroft:95}  \cite{adcroft:95}
258    
259  \begin{eqnarray}  \begin{eqnarray}
260  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-igw_stability}
261  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
262  \end{eqnarray}  \end{eqnarray}
263    
# Line 252  S_{c} = \frac{c_{g} \delta t}{ \Delta x} Line 265  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
265  stability limit of 0.25.  stability limit of 0.25.
266        
267  \subsection{Code Configuration}  \subsection{Code Configuration}
268    \label{www:tutorials}
269  \label{SEC:code_config}  \label{SEC:code_config}
270    
271  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
# Line 271  experiments. Below we describe the custo Line 285  experiments. Below we describe the custo
285  to these files associated with this experiment.  to these files associated with this experiment.
286    
287  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
288    \label{www:tutorials}
289    
290  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
291  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 282  are Line 297  are
297  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}
298  this line sets  this line sets
299  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
300  level in units of $^{\circ}$C.  level in units of $^{\circ}\mathrm{C}$.
301  The entries are ordered from surface to depth. For each  The entries are ordered from surface to depth. For each
302  depth level the initial and reference profiles will be uniform in  depth level the initial and reference profiles will be uniform in
303  $x$ and $y$.  $x$ and $y$.
# Line 473  notes. Line 488  notes.
488  \end{small}  \end{small}
489    
490  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
491    \label{www:tutorials}
492    
493  This file uses standard default values and does not contain  This file uses standard default values and does not contain
494  customizations for this experiment.  customizations for this experiment.
495    
496  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
497    \label{www:tutorials}
498    
499  This file uses standard default values and does not contain  This file uses standard default values and does not contain
500  customizations for this experiment.  customizations for this experiment.
501    
502  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
503    \label{www:tutorials}
504    
505  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
506  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
# Line 493  in MITgcm. The included matlab program { Line 511  in MITgcm. The included matlab program {
511  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
512    
513  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
514    \label{www:tutorials}
515    
516    
517  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
# Line 504  The included matlab program {\it input/g Line 523  The included matlab program {\it input/g
523  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
524    
525  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
526    \label{www:tutorials}
527    
528  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
529    
# Line 530  the vertical domain extent in grid point Line 550  the vertical domain extent in grid point
550  \end{small}  \end{small}
551    
552  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
553    \label{www:tutorials}
554    
555  This file uses standard default values and does not contain  This file uses standard default values and does not contain
556  customizations for this experiment.  customizations for this experiment.
557    
558    
559  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
560    \label{www:tutorials}
561    
562  This file uses standard default values and does not contain  This file uses standard default values and does not contain
563  customizations for this experiment.  customizations for this experiment.
564    
565  \subsubsection{Other Files }  \subsubsection{Other Files }
566    \label{www:tutorials}
567    
568  Other files relevant to this experiment are  Other files relevant to this experiment are
569  \begin{itemize}  \begin{itemize}
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